Classical limit of the tensor product of holomorphic discrete series representations

For three coadjoint orbits \(\mathcal {O}_1, \mathcal {O}_2\) and \(\mathcal {O}_3\) in \(\mathfrak {g}^*\) , the Corwin–Greenleaf function \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) is given by the number of \(G\) -orbits in \(\{(\lambda , \mu ) \in \mathcal {O}_1 \times \mathcal {O}_2 \, : \, \lambda + \mu \in \mathcal {O}_3 \}\) under the diagonal action. In the case where \(G\) is a simple Lie group of Hermitian type, we give an explicit formula of \(n(\mathcal {O}_1 \times \mathcal {O}_2, \mathcal {O}_3)\) for coadjoint orbits \(\mathcal {O}_1\) and \(\mathcal {O}_2\) that meet \(\left( [\mathfrak {k}, \mathfrak {k}] + \mathfrak {p}\right) ^{\perp }\) , and show that the formula is regarded as the ‘classical limit’ of a special case of Kobayashi’s multiplicity-free theorem (Progr. Math. 2007) in the branching law to symmetric pairs.     

Effect of morphology of thin DNA films on the electron stimulated desorption of anions

We present a comparison between the electron stimulated desorption (ESD) of anions from DNA samples prepared by lyophilization (an example of poorly organized or nonuniform films) and molecular self-assembly (well-ordered films). The lyophilization (or freeze- drying) method is perhaps the most frequently employed technique for forming DNA films for studies of low-energy electron (LEE) interactions leading to DNA damage; however, this technique usually produces nonuniform films with considerable clustering which may affect DNA configuration and enhance sample charging when the film is irradiated. Our results confirm the general validity of ESD measurements obtained with lyophilized samples, but also reveal limitations of lyophilization for LEE studies on DNA films. Specifically we observe some modulation of structures, associated with dissociative electron attachment, in the anion yield functions from different types of DNA film, confirming that conformational factors play a role in the LEE induced damage to DNA.     

Ab Initio Calculations of the Conformational Preferences of 1,3-Oxathiane S-Oxide and its Analogs Containing S and SE Atoms—Evidence for Stereoelectronic Interactions Associated with the Anomeric Effects

Abstract

Stereoelectronic interactions associated with the AE and also the conformational and structural properties of 1,3-oxathiane S-oxide (1), 1,3-dithiane S-oxide (2), 1,3-thiaselenane S-oxide (3), 1,3-oxaselenane Se-oxide (4), 1,3-thiaselenane Se-oxide (5), and 1,3-diselenane Se-oxide (6) were investigated using quantum mechanical methods. These compounds were fully optimized at the B3LYP/6 – 311 + G** and HF/6 – 311 + G** levels of theory. The Gibbs Free Energy, Enthalpy, and Entropy differences (i.e., ΔG, ΔH, and ΔS) between the axial and equatorial conformations were calculated at the B3LYP/6 – 311 + G** and HF/6 – 311 + G** levels of theory. The decrease of the AE is corresponding to the decreases of calculated Δ(G _ax – G _eq) value of the above mentioned compounds. The calculated AE values are more significant for the justification of the conformational dominances of the compounds than steric effects. In this work, the relations between the Anomeric Effects, donor and acceptor orbital energies, occupancies, structural parameters, dipole–dipole interactions, and conformational behavior of the compounds have been studied.     

Two-grid finite element method for the dual-permeability-Stokes fluid flow model

In this paper, two-grid finite element method for the steady dual-permeability-Stokes fluid flow model is proposed and analyzed. Dual-permeability-Stokes interface system has vast applications in many areas such as hydrocarbon recovery process, especially in hydraulically fractured tight/shale oil/gas reservoirs. Two-grid method is popular and convenient to solve a large multiphysics interface system by decoupling the coupled problem into several subproblems. Herein, the two-grid approach is used to reduce the coding task substantially, which provides computational flexibility without losing the approximate accuracy. Firstly, we solve a global problem through standard P_k ? P_k??1 ? P_k ? P_k finite elements on the coarse grid. After that, a coarse grid solution is applied for the decoupling between the interface terms and the mass exchange terms to solve three independent subproblems on the fine grid. The three independent parallel subproblems are the Stokes equations, the microfracture equations, and the matrix equations, respectively. Four numerical tests are presented to validate the numerical methods and illustrate the features of the dual-permeability-Stokes model.

     

Modeling and optimization of simultaneous degradation of rhodamine B and acid red 14 binary solution by homogeneous Fenton reaction: a chemometrics approach

This study aimed to propose a mathematical method to investigate and optimize the simultaneous elimination process of multiple organic pollutants using the Fenton process. Hence, the treatment of rhodamine B (RB) and acid red 14 (AR14) dyes in their binary solution was studied. Multivariate curve resolution alternating least square (MCR-ALS), a novel chemometric method, was applied along with correlation constraints to resolute the UV-Vis spectrophotometric data, enabling quantification of investigated dyes despite a high spectral overlapping. Response surface methodology was adopted to assess the model and optimize individual and interactive effects of three independent factors (Fe²⁺, H₂O₂ and initial pH) on the simultaneous elimination of RB and AR14. The values of the regression coefficient for RB and AR14 were determined as 98.48 and 98.67 percent, respectively, revealing the reliability of the obtained polynomial models to predict decolorization efficiencies. Desirability function was employed to optimize the independent variables to attain the highest possible degradation performance for both dyes in their binary solution. At the optimum point of operation ([Fe²⁺] = 143.88 mg/L, [H₂O₂] = 126.89 mg/L and pH = 3.71), degradation efficiencies of RB and AR14 were found as 81.58% and 80.22%, respectively, which were nearly identical to the experimental results.     

Silica supported sodium hydrogen sulfate(NaHSO4/SiO2): A mild and efficient reusable catalyst for the synthesis of aryl-14-H-dibenzo[a,j]xanthenes under solvent-free conditions

A simple and efficient procedure for the preparation of aryl-14-H-dibenzo[a,j]xanthenes by a one-pot condensation reaction of 2-naphthol and aryl aldehydes,in the presence of silica supported sodium hydrogen sulfate(NaHSO_4/SiO_2)as a catalyst and in the absence of solvent has been developed.The present method offers several advantages such as excellent yields,short reaction time (10-30 min),mild condition,simple work-up,and the use of a cheap and environmentally friendly catalyst with remarkable reusability.     

Complexes of some tervalent metals with <Emphasis Type="Italic">N</Emphasis>-alkyl(benzyl)nitrozohydroxylamine derivatives

Twenty two new complexes of some tervalent metals (aluminum, chromium, iron, and lanthanides) with nitrozohydroxylamine N-alkyl(benzyl) derivatives ML₃^m · nH₂O, (m = 1?5) were synthesized and isolated in a crystalline state. The crystal and molecular structures of the iron(III) complex with N-(2-fluorobenzyl)-N-nitrozohydroxylamine were determined by X-ray diffraction. An octahedral coordination of the central ion and a bidentate chelating coordination of the organic ligand were established. The spectral criteria of coordination of nitrozohydroxylamine alkyl(benzyl) derivatives were determined, and the complexation processes in solutions were studied.     

Conformational and structural study of N-nicotinyl N′, N″-bis(diisobutyl amine)phosphoric triamide

Single crystals of C5H4NC(O)NHP(O)[N(i-C4H9)2]2 were prepared and investigated by X-ray crystallography. Interestingly, four symmetrically independent conformers were detected in the structure of this compound by X-ray crystallography. The greatest difference in these conformers was different torsion angles. In all conformers, the phosphoryl and carbonyl groups showed anti-configurations, and the two terminal CH3 groups of each alkyl chain in amine parts have different spatial orientations due to their connection to a prochiral carbon atom. The diastereotopic protons of every CH2 moiety in amine groups also have different spatial orientations. Every conformer forms a centrosymmetric dimer with its own symmetrically generated analog via a hydrogen bond. The first conformer connects to others (A, B, and C) via electrostatic interactions and forms a tetramer. All hydrogen bonds and electrostatic interactions result in the formation of a three-dimensional polymeric network in the crystalline lattice of compound. To find the most stable conformer, density functional theory (DFT) calculations were performed. The computationally optimized geometric parameters are in good agreement with the experimental results. According to DFT calculations, B is the most stable conformer with energy of ?987714.07 kcal/mol. In all conformers the electron density of HOMO is localized on P=O and C=O oxygen atoms and some parts of amine groups, while LUMO is localized on the nicotinamide part of the molecule.     

Development of agricultural biotechnology and biosafety regulations used to assess the safety of genetically modified crops in Iran

Rapid progress in the application of biotechnological methodologies and development of genetically modified crops in Iran necessitated intensive efforts to establish proper organizations and prepare required rules and regulations at the national level to ensure safe application of biotechnology in all pertinent aspects. Practically, preparation of a national biotechnology strategic plan in the country coincided with development of a national biosafety framework that was the basis for the drafted biosafety law. Although biosafety measures were observed by researchers voluntarily, the establishment of national biosafety organizations since the year 2000 built a great capacity to deal with biosafety issues in the present and future time, particularly with respect to food and agricultural biotechnology.     

Synergistic effect of silica nanoparticles and charged surfactants in the formation and stability of submicron oil-in-water emulsions

The influence of hydrophilic silica nanoparticles on the emulsification of a triglyceride oil (Miglyol812) in the presence of charged surfactants (lecithin or oleylamine) and the long term stability of the resultant oil-in-water emulsions are reported. A synergistic effect of nanoparticles and surfactants in improving emulsification and stability to coalescence is evident only when the silica nanoparticles are initially added to the oil phase. When nanoparticles are included from the water phase, no synergistic stabilisation was observed due to electrostatic bridging or unfavourable attachment due to the repulsive electrostatic and hydration forces. Free energies of adsorption for silica nanoparticles at the oil-water interface calculated from experimentally determined interfacial tensions and three phase contact angles can be correlated to long-term emulsion stability only when silica is added from oil phase.